2.1 Number of Events

Lets look to see

Number of sports per year at the https://www.topendsports.com/events/summer/sports/number.htm

There is clearly an upward trend, but no seasonal pattern. The data is also a little choppy at the beginning. Part of the explanation is that the data points are not evenly spaced. Most Olympic games are 4 years apart, but a few of them are just 2 years apart, and during World War I and World War II there were 8-year and 12-year gaps, respectively. Since time series data should be evenly spaced over time, we’ll only look at data from 1948 on, when the Olympics started being held every 4 years without any interruptions.

Lets see if I can build a time series using our data.

Time Series:
Start = 1948 
End = 2020 
Frequency = 1 
     Year Num.Sports
1948 1948         17
1949 1952         17
1950 1956         17
1951 1960         17
1952 1964         19
1953 1968         18
1954 1972         21
1955 1976         21
1956 1980         21
1957 1984         21
1958 1988         23
1959 1992         25
1960 1996         26
1961 2000         28
1962 2004         28
1963 2008         28
1964 2012         26
1965 2016         28
1966 2020         33
1967 1948         17
1968 1952         17
1969 1956         17
1970 1960         17
1971 1964         19
1972 1968         18
1973 1972         21
1974 1976         21
1975 1980         21
1976 1984         21
1977 1988         23
1978 1992         25
1979 1996         26
1980 2000         28
1981 2004         28
1982 2008         28
1983 2012         26
1984 2016         28
 [ reached getOption("max.print") -- omitted 36 rows ]

2.2 Creating the models

I’m going to try 4 different models.

\[ y_{\text{linear}}(x) = ax+b \\ y_{\text{quadratic}}(x) = ax^2 + bx + c \\ y_{\text{exponential}}(x) = a\exp(bx) + c \\ y_{\text{cubic}}(x) = ax^3 + bx^2 + cx + d \]

And I’ll be able to use ANOVA to test the nested models: linear vs quadratic, and exponential growth vs s-curve (sigmoid).

These models all look fairly similar. Lets check using ANOVA.

Res.Df	Res.Sum Sq	Df	Sum Sq	F value	Pr(>F)
17	33.33158	NA	NA	NA	NA
16	30.41244	1	2.919136	1.535759	0.2331213
16	32.28073	0	0.000000	NA	NA
15	29.04971	1	3.231026	1.668361	0.2160269

Linear model preferred. Nothing gained from adding complexity to the model.

Lets look at the top 10 sports by number of participants.

                  Sport  freq
3             Athletics 19641
41             Swimming 14094
22           Gymnastics 13175
12 Cross Country Skiing  6134
1         Alpine Skiing  5649
14              Cycling  5567
31               Rowing  5325
34             Shooting  5307
17              Fencing  5073
11             Canoeing  4198

	Sport	freq
3	Athletics	19641
41	Swimming	14094
22	Gymnastics	13175
12	Cross Country Skiing	6134
1	Alpine Skiing	5649
14	Cycling	5567
31	Rowing	5325
34	Shooting	5307
17	Fencing	5073
11	Canoeing	4198

I need to subset the data because I keep getting the following error: “Error: vector memory exhausted (limit reached?)”. I will drop the following variables: NOC, Decade, ID, First.Name, Name, BMI, BMI.Category, Games, City, Event. I will only focus on the top ten sports.

[1] 151977

[1] 58693

Lets try making logistic regression models for Weight and Height.

  Year Mean_Weight StdDev_Weight Mean_Height StdDev_Height    Sport Sex
1 1924    64.00000      0.000000    167.0000      0.000000 Swimming   F
2 1956    61.00000      4.780914    169.7333      3.634491 Swimming   F
3 1960    62.73469      5.619073    169.3469      6.839076 Swimming   F
4 1964    63.06000      6.466270    171.3600      4.378799 Swimming   F
5 1968    62.45455      5.361348    170.3636      4.583033 Swimming   F
6 1972    60.23611      5.491333    170.3889      4.949194 Swimming   F

'data.frame':   339 obs. of  7 variables:
 $ Year         : int  1924 1956 1960 1964 1968 1972 1976 1980 1984 1988 ...
 $ Mean_Weight  : num  64 61 62.7 63.1 62.5 ...
 $ StdDev_Weight: num  0 4.78 5.62 6.47 5.36 ...
 $ Mean_Height  : num  167 170 169 171 170 ...
 $ StdDev_Height: num  0 3.63 6.84 4.38 4.58 ...
 $ Sport        : Factor w/ 10 levels "Basketball","Canoeing",..: 9 9 9 9 9 9 9 9 9 9 ...
 $ Sex          : Factor w/ 2 levels "F","M": 1 1 1 1 1 1 1 1 1 1 ...

  Year Mean_Weight StdDev_Weight Mean_Height StdDev_Height    Sport Sex
1 1924    64.00000      0.000000    167.0000      0.000000 Swimming   F
2 1956    61.00000      4.780914    169.7333      3.634491 Swimming   F
3 1960    62.73469      5.619073    169.3469      6.839076 Swimming   F
4 1964    63.06000      6.466270    171.3600      4.378799 Swimming   F
5 1968    62.45455      5.361348    170.3636      4.583033 Swimming   F
6 1972    60.23611      5.491333    170.3889      4.949194 Swimming   F

Medal	mean
Bronze	25.55859
Gold	25.28269
No Medal	24.93049
Silver	25.48383

# A tibble: 6 x 3
# Groups:   Year [3]
   Year Sex   mean.Age
  <int> <fct>    <dbl>
1  1960 F         21.6
2  1960 M         26.0
3  1964 F         21.5
4  1964 M         25.7
5  1968 F         20.5
6  1968 M         25.1

2.3 Swimming

2.4 Athletics

2.5 Gymnastics

2.6 Rowing

2.7 Baskeball

2.8 Softball

2.9 Fencing